Having grown up in NYC, "crossroads of the world", and lived through the mid 20th Century, I consider myself a "primary source" on such a matter. :-) :
As far as that period is concerned, at least in the Western World, the answer is a resounding No - it was not less exclusively limited to women - on the contrary. A man with painted fingernails? Few things could have been more bizarre. (Obviously I'm talking about public, 'mainstream society', not the sub-cultures of homosexuals, etc, where I imagine things might have been different)
By way of analogy, consider hair styles: When the Beatles became big in 1962-3 (I was a teenager at that time) they were notorious internationally for their "long hair". Yet when you look back on their early photos, by today's standards you see nothing unusual whatsoever about their hair styles. The contemporary world has become far more open-minded about "male plumage" compared to the relatively puritanical and dour mid 20th century.
I also found this (I have not yet vetted the source) @ http://redroom.com/member/frank-sanello/writing/hermann-goring-nazi-war-criminal-drug-addict-transvestite. From this source it seems quite obvious that Göring's behavior was by no means the norm:
World War II in Drag
Göring engaged in other aberrant behavior that apparently the Gestapo
didn’t think of using to blackmail him. Visiting generals at Göring's
palatial hunting lodge in suburban Berlin were shocked by their host's
The second most powerful man in the Third Reich greeted guests wearing
a kimono, rouge, lipstick, pancake makeup, lacquered fingernail
polish, and women’s jewelry while padding about in pink, fur-lined
A Report on the Banality of Evil, the subtitle of Hannah Arendt's book
about Adolf Eichmann's trial in Israel in 1961, comes to mind when
Göring's concept of casual dress is described.
Although many Nazis were gay, especially the purged Storm Troopers,
Göring was a heterosexual transvestite who married twice, fathered a
daughter, and had numerous extramarital affairs ‒ with women.
Göring’s custom of painting his finger nails continued in prison
during his post-war trial at Nuremberg until the martinet American
warden ordered his prisoner to remove the polish..
Prior to Germany’s defeat, Göring’s decadent lifestyle and
incapacitating drug use were noted by his ally, SS chief Heinrich
Himmler. When Speer tried to enlist Göring’s support in a power
struggle against Hitler’s private secretary, Martin Bormann, Himmler
told Speer not to waste his time. “I think it would very unwise of you
to try to activate the Reichsmarschall again!”
Be that as it may, all the sources, (there are a many references to Göring's affectation, which became quite public when he was tried after the war) including the one kmlawson based the question on, single out Göring - I think that itself answers the question: It was a peculiar habit of Göring - not the norm among Nazi officers or anyone else.
In addition, Sanello's account: "wearing a kimono, rouge, lipstick, pancake makeup, lacquered fingernail polish, and women’s jewelry while padding about in pink, fur-lined bunny slippers" indicates that regarding Göring, the issue was not just painted nails, which appears to have been indeed been a custom among warrior and aristocratic classes during certain periods of history, as cited by
kmlawson in his erudite answer: Göring's behavior appears to have been out and out cross dressing.
Still, one could surmise that Göring had adopted the customs of earlier societies and decided that expanding on such habits behooved him, considering his very prominent position in the Third Reich.